# How to find position of a point based on known angle, radius and center of rotation?

I'm having a hard time remembering trig, and I have spent some time trying to solve this.

How do I find the coordinate of a point on a circle for certain angle if we know radius of circle and a center of circle coordinate?

## 2 Answers

For a given angle $\theta$ and a circle of radius $r$ and center $(h, k)$, recall that we can determine the Cartesian coordinates $(x, y)$ of the point on the circle determined by $\theta$ and $r$, where $$x = h + r \cos \theta,\;\;y = k + r\sin \theta$$

• I'm not sure I understand, but how is this dependent on the coordinate of the circle center? Won't it be same for circle with same radius on any point? Aug 25, 2013 at 16:35
• If the circle's center is not the origin, then we add $h$ to $x = r\cos\theta$ and $k$ to $y = r\sin\theta$. Aug 25, 2013 at 16:38
• centres may not be same. Aug 25, 2013 at 16:40
• how would the formula look like for a 3D circle? Sep 6, 2016 at 9:10

if the centre of the answer circle is $(h,k)$,angle $\theta$,and radius $r$,then position of point is $$(h + r\cos\theta, k + r\sin\theta)$$